Concrete Countertop - please help  

A friend had a similar problem with her concrete countertop.
She had a concrete installer come in with a grinder, and smooth it out. She was told that wet concrete will not properly adhere to dry concrete. Her kitchen was a bit dusty for a while. Is the rough patch in an obvious spot? Can you hide it with a small appliance?
But maybe I'm wrong,
Aunt Mark

Mark is right. New concrete w...
Mark is right. New concrete will not adhere to existing. You will have to grind it.

Concrete
When we remodeled our kitchen we did concrete counter tops also. If you can....get them outside as when you grind you'll be using a wet grinder and indeed, it will be WET. I have photos of the two of us wearing big plastic garbage bags so as not to get soaked. The concrete 'go to' guy is Chen. He will tell you to forget about grinding inside.....Just saying...

I don't like
the idea of grinding out an imperfection. The result will be a dip in the surface, inevitably.
This repair should have been made by the maker of the countertop -- and they should be willing now to help you achieve an acceptable repair, including but not limited to providing the necessary materials. One possibility would be to apply and level some epoxy paste, onto which some dust from the same kind of concrete has been added as a topping (?). You'd have to experiment with the material to choose the right color of epoxy.
As with wood and other materials, letting the natural color of the material be the finished color -- with the possible help of a clear coating -- is the best route to a satisfactory color. The most successful colored concrete has the color made integral with the material. Staining an variegated material like concrete is risky as to finished appearance. This problem would be aggravated by the addition of a patch repair.
So, another possibility -- especially if you want a different color -- would be to apply a topcoat to the entire top. Liquid epoxy flooring is now available; that would be one avenue to explore. This might be a two-step process: fill voids and low places with the appropriate filler, then top with the final coat.

I don't this is a good idea of concrete on top of concrete.I think you should consult an engineer who is in remodelling of kitchen.As they can give you a better suggestion.I recently changed my cabinets and counter tops of kitchen from denver renovations.They have a idea how to handle these things.

Your original post was from a year ago.  What did you do eventually?  You mentioned "before I stain" and that seems curious as the stain goes into the concrete mix.  Did you mean before you put final conditioner on??